Stepwise Process to Use Vernier Callipers for Accurate Diameter Measurements
Vernier caliper was invented by a French Mathematician named Pierre Vernier in 1631. It is an instrument for making very accurate measurements.
Vernier caliper works on the principle that vernier scale uses the alignment of line segments that can be displaced by small amounts for the measurement.
It uses two scales viz: the main scale and the auxiliary scale. The main is similar to the ruler, while the vernier scale slides on the main scale that makes readings to the fraction of a division on the main scale.
Vernier Caliper Measurement
Vernier calipers are used in the two following areas:
In scientific laboratories.
For quality control measurements.
Vernier calipers measure the diameter of small spherical objects, depth, and length very accurately, that’s why they are called Precision measuring instruments.
Parts of Vernier Caliper
A vernier caliper has the following parts:
Outside Jaws: To measure the external diameter of a small spherical object.
Inside Jaws: To measure the internal dimension of a small spherical object.
Measuring Depth Probe: For measuring the depth of objects.
Main Scale: In cm.
Main Scale: in inches.
Vernier Scales: In cm.
Vernier Scales: In inches.
Retainer: To block the movable part.
(Image will be uploaded soon)
The formula for the vernier caliper measurement is:
Measurement = MSR + (VSR * L.C.)
The least count of the vernier caliper is:
L.C. measurement = 1 MSD - 1VSD
Objective: To ascertain the diameter of a spherical body.
Apparatus/Materials Required:
Spherical object viz: a spherical marble piece, or a pendulum bob.
Vernier Caliper.
Magnifying glass.
Theory
The smallest distance that can be measured along with the distance is the least count or L.C. L.C.is the difference between one main scale division and one vernier scale division.
The formula for the same is given below:
n (MSD) = (n - 1) VSD
Here,
MSD = Main scale division.
VSD = Vernier scale division.
Measure Diameter of a Small Spherical using Vernier’s Calipers
Procedure to measure diameter of a small spherical cylindrical body using vernier’s calipers is as follows:
Check with the instrument, keep both the jaws closed and make sure that the zero of the main scale and the vernier scale coincide with each other.
Now, use a magnifying glass to check whether we were able to coincide the two zeroes and then check the number of divisions coinciding with each other.
Release the movable jaw by opening the screw. Put the cylindrical spherical body inside these jaws but not tightly. Make sure that these jaws lie perpendicular to the body. Slowly and gently tighten the screw to adjust the instrument in the position of the body.
Note the position of zero of the vernier scale against the main scale ( we won’t get the perfect coincide). Now, read the reading on the main scale division to the left of the zero marks of the vernier scale (V.S.).
Find the precise coincidence of the main scale division with the vernier scale division in the vernier window, moving from the left end to the right and then note down number ‘M’.
Multiply the least count of the instrument with the number ‘M’. Add the acquired product to the main scale reading noted in step 4. We need to make sure that the product so obtained is to be converted into proper units for addition.
Now, repeat the steps from 3 to 6, do the measurements along with the different positions of the curved surface of the sphere, and obtain at least three readings in each case.
Finally, record all the observations in a tabular form and apply the arithmetic mean of the correct readings of the diameter of the body.
What Did You Observe?
We observed the following things:
Main scale 1 mm = 0.1 cm.
Number of vernier scale division (M) = 10.
If 10 vernier scale divisions are equal to 9 main scale divisions, then:
1 vernier scale division is equal to 0.9 main scale divisions.
Vernier constant = 1 MSD - 1 VSD = 1 - 0.9 = 0.1 main scale divisions
So, we get the vernier constant as 0.1 MSD = 0.1 mm = 0.01 cm.
So, observed reading - (± Zero reading) = True reading.
So, this was the procedure to measure the diameter of a small spherical. Now, record all the readings in the table given below:
The Table form for Noting the Details of Measuring the Diameter of a Small Spherical is:
Zero error = ± ……cm.
Mean observed diameter in cm = ……
The formula for the corrected diameter is the difference between the mean observed diameter and the zero error.
Our final result is:
The diameter of the cylinder or the sphere in…...cm.
Types of Vernier caliper
Flat Edge Vernier Caliper - This kind of vernier is used for basic tasks. We can measure the length, breadth, diameter and thickness of a task, among other things. Because the jib on its edge is of a unique kind, it may also be used to obtain the inner measurement. However, the job breadth must be deducted from that measurement.
Knife Edge Vernier Caliper - This Vernier caliper’s edge is as sharp as a knife. This vernier caliper is useful for measuring tiny spaces, the distance between bolt holes, and so on. Its basic flaw is that the thin edge of its jaw wears down fast, causing it to give incorrect measurements.
Vernier Gear Tooth Caliper - This is a unique tool that resembles the combination of two vernier calipers. It has two distinct scales, vertical and horizontal. The thickness of a gear tooth may be calculated using a vernier caliper and its pitch circle.
Vernier Depth Gauge - This tool is used to gauge the depth of a job's slot, hole, or groove. This depth gauge is created from a thin beam, similar to a narrow rule. It has an inch or metric system for the main scale and vernier scale. This is nearly identical to a vernier caliper. However, instead of a jaw, it has a flat-shaped base, as illustrated in the figure.
Vernier Height Gauge - It's used to take accurate measurements of a job's height or to mark it. It's comparable to a vernier caliper, but it's utilized by connecting certain extra attachments to it. The length of the beam is still fixed to a base. The height of a task is measured or marked with an offset scriber mounted on the beam itself.
Vernier Dial Caliper - When using a standard vernier caliper, there is a potential of making a mistake when it comes to clear reading. Vernier Dial calipers are now often used for this purpose. It has a graduation dial in place of the vernier scale, as indicated in the illustration. It can measure in both inches and millimetres, just as vernier calipers. Rack and pinion are employed in it, same as in a dial test indicator. The rack is still attached to the main scale, which is connected to the dial's pinion.
Precautions
When using a vernier caliper, take the following precautions into account:
The parallax error is the most prevalent type of mistake. When an object is seen from a different angle, this mistake happens. This causes the object to look in a little different location than it actually is, which can cause us to misread a measuring scale. When taking the Main Scale reading and the Vernier Coincidence, the observer should place his eyes exactly above the scale to eliminate this inaccuracy.
While measuring, make sure to take all of your readings in the same unit system. If any measurements are collected in a different system's unit, they must be converted to the correct units before being utilized in calculations.
When gripping the object to be measured, avoid using too much force on the jaws. The thing should be gently held between the jaws at all times.
Make sure the vernier caliper does not have a zero error before taking any measurements. If the error is zero, the necessary connections should be made.
Measuring precision is mostly determined by two senses:
Sense of sight
Sense of touch
A cloth soaked in cleaning oil should be used to clean and dry the object's surface and instrument cover.
Loosen the vernier caliper locking key and ensure there is no friction between the scales while rotating the vernier caliper’s jaws.
Additional measures should be required in the case of a digital vernier caliper: Press the on/off button after bringing the jaws into contact with each other.
Check the reading and make sure it is zero.
Move the slider and check whether all the buttons and the LCD display are working properly.
FAQs on Measure the Diameter of a Small Spherical Body Using Vernier Callipers
1. What is the step-by-step procedure to measure the diameter of a small spherical body using a Vernier calliper for the 2025-26 syllabus?
To measure the diameter of a small spherical body, follow these essential steps:
- First, determine the least count (LC) of the Vernier calliper and check for any zero error.
- Gently place the spherical body between the lower jaws of the calliper, ensuring it is held firmly but not compressed.
- Note the main scale reading (MSR), which is the reading on the main scale just to the left of the zero mark on the vernier scale.
- Identify the vernier scale division (VSD) that perfectly coincides with any division on the main scale. This is the vernier scale coincidence (VSC).
- Calculate the total observed diameter using the formula: Total Reading = MSR + (VSC × LC).
- Finally, apply the zero error correction (subtract positive error, add negative error) to get the correct diameter.
2. What is the 'least count' of a Vernier calliper and why is its definition important?
The least count of a Vernier calliper is the smallest measurement that can be accurately taken with the instrument. It represents the difference between the value of one smallest division on the main scale and one smallest division on the vernier scale. Its importance lies in determining the precision of the instrument; a smaller least count means a more precise measurement. It is calculated as: LC = 1 Main Scale Division (MSD) - 1 Vernier Scale Division (VSD).
3. Why is a Vernier calliper a better choice than a regular metre scale for this experiment?
A Vernier calliper is preferred over a regular metre scale because of its higher precision. A typical metre scale has a least count of 1 mm, which is often too large for accurately measuring small objects like a sphere or a wire. A Vernier calliper, with a least count of 0.1 mm or even 0.02 mm, allows for a much more accurate and reliable measurement, significantly reducing the percentage error in the final result.
4. What is a 'zero error' in a Vernier calliper, and how does it affect the final measurement?
A zero error occurs when the zero mark of the main scale does not coincide with the zero mark of the vernier scale when the jaws are fully closed. It affects the accuracy of all measurements taken.
- Positive Zero Error: Occurs if the vernier scale's zero is to the right of the main scale's zero. The observed reading will be higher than the actual value, so the error must be subtracted from the final reading.
- Negative Zero Error: Occurs if the vernier scale's zero is to the left of the main scale's zero. The observed reading will be lower than the actual value, so the error's magnitude must be added to the final reading.
5. How does 'parallax error' happen while reading a Vernier calliper, and what is the correct technique to avoid it?
Parallax error occurs when the observer's eye is not positioned directly perpendicular to the measurement mark on the scale. This incorrect line of sight causes the reading to appear shifted, leading to an inaccurate measurement. To avoid this, you must always position your eye directly above the coinciding division so that your line of sight is exactly at a right angle (90°) to the scale.
6. Why is it important to measure the sphere's diameter at different orientations and then calculate the average?
It is important to measure the diameter at multiple different positions because a small spherical body may not be perfectly uniform; it might have slight surface irregularities or not be a perfect sphere. By taking several readings from different orientations and calculating the mean diameter, you effectively minimise the impact of these random errors and local imperfections. This process yields a more accurate and representative value for the sphere's true average diameter.
7. Besides measuring a sphere's external diameter, what are two other types of measurements a Vernier calliper can perform?
A Vernier calliper is a versatile instrument capable of several types of measurements:
- Internal Diameter: Using the smaller, upper jaws, it can accurately measure the internal diameter of a hollow object, such as a pipe or a beaker.
- Depth: Using the thin sliding strip that extends from the end of the main scale, it can measure the depth of a hole or the step between two surfaces.
